Multiple-core optical fiber with coupling between the cores

ABSTRACT

An optical fiber includes a cladding, a first core, and a second core. At least one of the first core and the second core is hollow and is substantially surrounded by the cladding. At least a portion of the first core is generally parallel to and spaced from at least a portion of the second core. The optical fiber includes a defect substantially surrounded by the cladding, the defect increasing a coupling coefficient between the first core and the second core.

CLAIM OF PRIORITY

This application is a continuation from U.S. patent application Ser. No.11/681,019, filed Mar. 1, 2007 and incorporated in its entirety byreference herein, and which claims the benefit of U.S. ProvisionalPatent Application No. 60/778,229, filed Mar. 2, 2006, which isincorporated in its entirety by reference herein.

BACKGROUND

1. Field of the Invention

This application relates generally to optical devices utilizingphotonic-bandgap fibers.

2. Description of the Related Art

Photonic-crystal fibers have been the subject of much interest anddevelopments in recent years. (See, e.g., J. Broeng et al., “Photoniccrystal fibers. A new class of optical waveguides,” Optical FiberTechnology, Vol. 5, pages 305-330 (1999); J. C. Knight et al. “Photoniccrystals as optical fibers-physics and applications,” Optical Materials,Vol. 11, pages 143-151 (1999); R. S. Windeler et al., “Silica-airmicrostructured fibers: Properties and applications,” Optical FiberCommunications conference, San Diego, Calif. (1999).) Because of theirunique properties, including low optical nonlinearities and goodtemperature stability, hollow-core photonic-bandgap fibers (PBFs) arefinding interesting applications as sensors and delivery systems. (See,e.g., V. Dangui et al., “Phase sensitivity to temperature of thefundamental mode in air-guiding photonic-band gap fibers,” OpticsExpress, Vol. 13, pages 6669-6684 (2005); H. K. Kim et al. “Fiber-opticgyroscope using an air-core photonic-bandgap fiber,” Proceeding ofSPIE—The International Society for Optical Engineering, 17thInternational Conference on Optical Fibre Sensor, OFS-17, Vol. 5855,pages 198-200 (2003).) In addition, the propagation loss in hollow-corePBFs is not limited by the core material, and it is expected that thepropagation loss can be exceedingly low. The hollow core can be filledwith air, or other gases or combinations of gases to generate thedesired light-matter interaction. With further research andimprovements, hollow-core PBFs could well replace conventional fibers inoptical communication links.

One of the most important components of fiber circuits for theseapplications is the optical fiber coupler. Fiber circuits utilizinghollow-core PBFs can be readily assembled using conventional (i.e.,solid-core) fiber couplers, which can be either butt-coupled or splicedto the hollow-core PBF. However, this approach suffers from variousshortcomings. Butt-coupled junctions often do not provide sufficientmechanical stability, and splices of dissimilar fibers can introducesignificant amount of back-reflection and associated loss, as well asbeing somewhat difficult to fabricate. In addition, the use of aconventional fiber coupler introduces a length of solid-core fiber inthe hollow-core fiber circuit, thereby re-introducing dispersion andnonlinearity into the fiber circuit and negating some of the benefits ofusing the hollow-core PBFs.

Examples of applications in which these effects can be detrimentalinclude, but are not limited to, delivery by a hollow-core PBF ofpulse-distortion-free high-peak-power pulses for fluorescence imaging(see, e.g., T. P. Hansen et al., “All-fiber chirped pulse amplificationusing highly-dispersive air-core photonic bandgap fiber,” OpticsExpress, Vol., 11, pages 2832-2837 (2003)) and in hollow-core PBFgyroscopes (see, e.g., R. A. Bergh et al., “Single-mode Fibre OpticDirectional Coupler,” Electronics Letters, Vol. 16, pages 260-261(1980); J. V. Wright, “Variational Analysis of Fused Tapered Couplers,”Electronics Letters, Vol. 21, pages 1064-1065 (1985).), where the Kerreffect is advantageously minimized and additional lengths of solid-corefibers are to be avoided.

SUMMARY

In certain embodiments, an optical coupler is provided. The opticalcoupler comprises a first optical port, a second optical port, a thirdoptical port, and a fourth optical port. The optical coupler furthercomprises a photonic-bandgap fiber comprises a cladding, a first core,and a second core. The cladding comprises a material with a firstrefractive index and regions within the cladding. The regions have asecond refractive index lower than the first refractive index. The firstcore is substantially surrounded by the cladding. The first core isoptically coupled to the first optical port and to the second opticalport. The second core is substantially surrounded by the cladding. Thesecond core is optically coupled to the third optical port and to thefourth optical port. At least a portion of the first core is generallyparallel to and spaced from at least a portion of the second core suchthat the first core is optically coupled to the second core. The firstcore, the second core, or both the first core and the second core ishollow.

In certain embodiments, a method for using a photonic-bandgap fiber isprovided. The method comprises providing a photonic-bandgap fibercomprising a cladding, a first core, and a second core. The claddingcomprises a material with a first refractive index and regions withinthe cladding. The regions have a second refractive index lower than thefirst refractive index. The first core is substantially surrounded bythe cladding. The second core is substantially surrounded by thecladding. The first core is spaced from the second core such that thefirst core is optically coupled to the second core. The method furthercomprises coupling light between the first core and the second core.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A schematically illustrates an example optical coupler inaccordance with certain embodiments described herein.

FIG. 1B schematically illustrates an example fiber coupler formed byside polishing two hollow-core photonic-bandgap fibers mounted on silicablocks.

FIG. 1C schematically illustrates a cross-sectional view of an exampletwo-core photonic-bandgap fiber (PBF) in accordance with certainembodiments described herein.

FIG. 2 illustrates dispersion curves of the four fundamental modes of anexample two-core PBF structure with R=0.8Λ, ρ=0.47Λ, and d=3Λ.

FIGS. 3A-3B illustrate contour and logarithmic scale plots,respectively, of the odd mode, x-polarized intensity profile of thetwo-core PBF (d=3Λ) at λ=0.6Λ.

FIGS. 3C-3D illustrate contour and logarithmic scale plots,respectively, of the even mode, x-polarized intensity profile of thetwo-core PBF (d=3Λ) at λ=0.6Λ.

FIGS. 3E-3F illustrate contour and logarithmic scale plots,respectively, of the odd mode, y-polarized intensity profile of thetwo-core PBF (d=3Λ) at λ=0.6Λ.

FIGS. 3G-3H illustrate contour and logarithmic scale plots,respectively, of the even mode, y-polarized intensity profile of thetwo-core PBF (d=3Λ) at λ=0.6Λ.

FIGS. 4A-4D illustrate the contour intensity profiles of the (i) odd,x-polarized, (ii) even, x-polarized, (iii) odd, y-polarized, and (iv)even, y-polarized modes for d=4Λ at λ=0.6Λ, respectively.

FIG. 5 illustrates the dispersion curves of the four fundamental modesof another example two-core PBF structure with R=0.8Λ, ρ=0.47Λ, andd=4Λ.

FIG. 6 illustrates the normalized coupling length L_(C)/Λ as a functionof wavelength for an example two-core PBF with R=0.8Λ, ρ=0.47Λ, and dvarying from Λ to 6Λ.

FIG. 7A illustrates the coupling ratios for x- and y-polarization for anexample two-core PBF with a crystal period Λ=2.6 microns, a bandgapcentered around 1.55 microns, d=3Λ=7.8 microns, and a length L=10.5millimeters.

FIG. 7B illustrates the coupling ratios of FIG. 7A in the region of 1522nanometers.

FIG. 7C illustrates the coupling ratios of FIG. 7A in the region of 1569nanometers.

FIG. 7D illustrates the coupling ratios of FIG. 7A in the region of 1599nanometers.

FIGS. 8A and 8B illustrate the transmission as a function of wavelengthfor both polarizations in example two-core PBFs with lengths of 2millimeters and 3 millimeters, respectively.

FIG. 9 illustrates the x- and y-polarization coupling lengths forvarious values of the core radius R as functions of wavelength.

FIGS. 10A and 10B schematically illustrate two example two-core PBFscompatible with certain embodiments described herein.

FIG. 11 illustrates the birefringence as a function of the defect radiusfor the point defect of FIG. 10A with a core separation of 4 crystalspatial periods.

FIG. 12 illustrates the birefringence as a function of the defect radiusfor the point defect of FIG. 10A with a core separation of 6 crystalspatial periods.

FIG. 13 illustrates the birefringence as a function of the defect radiusfor the line defect of FIG. 10B with a core separation of 6 crystalspatial periods.

DETAILED DESCRIPTION

FIG. 1A schematically illustrates an example optical coupler 100 inaccordance with certain embodiments described herein. The opticalcoupler 100 comprises a first optical port 110, a second optical port120, a third optical port 130, and a fourth optical port 140. Theoptical coupler 100 further comprises a two-core photonic-bandgap fiber(PBF) 150 comprising a cladding 160, a first core 170, and a second core180. The first core 170 is optically coupled to the first optical port110 and to the second optical port 120. The second core 180 is opticallycoupled to the third optical port 130 and to the fourth optical port140. In certain embodiments, the first optical port 110 comprises afirst portion of the first core 170, and the second optical port 120comprises a second portion of the first core 170. In certainembodiments, the third optical port 130 comprises a first portion of thesecond core 180, and the fourth optical port 140 comprises a secondportion of the second core 180. Persons skilled in the art can identifyappropriate means or techniques for splicing or butt-coupling thetwo-core PBF to other portions of an optical system in accordance withcertain embodiments described herein.

Two hollow-core photonic-bandgap fibers (PBFs) can be coupled to eachother by using the same technologies developed for coupling solid-corefibers. For example, as described more fully below, in certainembodiments, a two-core PBF coupler can be fabricated with two hollowcores, each of which is substantially surrounded by a cladding. Incertain other embodiments, other technologies can be used to fabricate ahollow two-core PBF coupler, including but not limited to, side-by-sidecoupling of polished hollow-core PBFs, fusing of two hollow-core PBFstogether, and utilizing micro-optic beam splitters. FIG. 1Bschematically illustrates an example fiber coupler 100 formed by sidepolishing two hollow-core PBFs 102, 104 mounted on silica blocks.Micropositioners can be used to position both hollow-core PBFs 102, 104together, and by controlling the distance and/or angle of the PBFs 102,104, a tunable device can be fabricated.

FIG. 1C schematically illustrates a cross-sectional view of the two-corePBF 150 in a plane generally perpendicular to a longitudinal axis of thetwo-core PBF 150. The cladding 160 comprises a material 162 with a firstrefractive index and regions 164 within the cladding 160. The regions164 have a second refractive index lower than the first refractiveindex. FIG. 1B does not show all of the regions 164. In certainembodiments, the first core 170 and the second core 180 aresubstantially identical to one another (e.g., twin-core PBF).

In certain embodiments, the material 162 comprises silica, while incertain other embodiments, the material 162 comprises another solidmaterial or a multiplicity of solid materials (e.g, high-index glassessuch as chalcogenides, or polymers such as PMMA). In certainembodiments, at least one or both of the first core 170 and the secondcore 180 is hollow. In certain embodiments, the regions 164 are hollow.As used herein, the term “hollow” is used in its broadest sense,including being empty or filled with a gaseous material. For example,the first core 170, the second core 180, and the regions 164 of certainembodiments are filled with a gaseous second material (e.g., air), whichcan be at atmospheric pressure, at higher pressures, or at lowerpressures (e.g., at vacuum).

Various shapes and patterns of the regions 164 of the cladding 160 arecompatible with certain embodiments described herein. The regions 164can have circular cross-sections (with radius ρ), as schematicallyillustrated by FIG. 1B, but other shapes of these regions 164 (e.g.,elliptical, hexagonal, non-geometrical, or non-symmetric) are alsocompatible with certain embodiments described herein. As schematicallyillustrated by FIG. 1B, the regions 164 each have a respective centerand adjacent regions 164 are spaced apart by a center-to-center distanceΛ. In certain embodiments, the regions 164 of the cladding 160 arecylindrical extending along the longitudinal axis of the two-core PBF150. In certain embodiments, the regions 164 are generally identical toone another and are in a periodic, triangular pattern. In addition, theregions 164 can be in other patterns (e.g., hexagonal patterns, squarepatterns, non-periodic patterns, etc.).

In certain embodiments, one or both of the cores 170, 180 has a circularcross-section (with a radius R), as schematically illustrated by FIG.1B. However, other cross-sectional shapes for the first core 170 and thesecond core 180 are also compatible with certain embodiments describedherein. In certain embodiments, the first core 170 and the second core180 each have a respective center, and the centers are separated along alattice vector of the regions 164 of the cladding 160. In certain suchembodiments in which the cores 170, 180 are centered on two regions 164,the core-to-core separation d is a multiple of the crystal spatialperiod Λ, i.e., d=mΛ, where m is an integer. In certain suchembodiments, the integer m is even, while in certain other embodiments,the integer m is odd.

The first and second refractive indices are selected in certainembodiments such that each of the cores 170, 180 supports a guided modevia the photonic-bandgap effect. This implies that the second refractiveindex of the regions 164 is lower than the first refractive index of thematerial 162, and that the difference between these indices is largeenough to support guided modes. In certain embodiments, neither of thecores 170, 180 comprises a core ring, while in certain otherembodiments, one or both of the first core 170 and the second core 180comprises a core ring.

Coupling between the first core 170 and the second core 180 cangenerally be described by either coupled-mode or normal-mode theory. Incoupled-mode theory, when light is launched into the fundamental mode ofthe first core 170, the evanescent field of the light extends into theadjacent second core 180 and excites the fundamental mode of the secondcore 180, which results in the energy of the light graduallytransferring into the second core 180.

In normal-mode theory, the structure is viewed as a two-core waveguide,which supports four non-degenerate eigemnodes: an even (or symmetric)mode and an odd (or antisymmetric) mode for each of the two orthogonallinear polarizations. When light of a given polarization is launchedinto one of the cores 170, 180, it excites the even and odd modes ofthis polarization with almost equal power. Because these twonon-degenerate modes have different phase velocities, as they propagatealong the fiber, they accumulate a phase shift. After a certain length,called the coupling length or beat length, this phase shift reaches πradians, so the two modes are out of phase from one another, and theyinterfere destructively in the original core and constructively in theother core. Thus, at the beat length, the energy of the light has beencoupled from one core to the other core. It can be shown that the beatlength is proportional to the reciprocal of the effective index mismatchbetween the even modes and the odd modes.

To model the coupling properties of the two-core PBE structure, anumerical simulator can be used to calculate the effective indices ofthe two fundamental eigenmodes supported by the two cores 170, 180. Suchnumerical simulations, performed using the Stanford Photonic-BandgapFiber (SPBF) code, are described more fully below. The numericalsimulations used a finite-difference method to solve a vectorialtransverse-magnetic-field equation in a matrix form to quickly andaccurately calculate the effective index, electric fields, and magneticfields of the four fundamental eigenmodes of a fiber of arbitrary indexprofile. (See, e.g., V. Dangui et al., “A fast and accurate numericaltool to model the mode properties of photonic-bandgap fibers,” OpticalFiber Conference Technical Digest, Anaheim, Calif. (2005).) Only onequadrant of the two-core PBF structure was modeled, and the fields inthe other quadrants were reconstructed by symmetry. The code's boundaryconditions imposed that all fields are zero outside of the simulationarea. The code was run with a step size of Λ/50 and a window size (forone quadrant) of 11Λ×11Λ (10 rows of cladding regions plus an outercladding of solid silica about λ/2 thick). On a 3.2-GHz personalcomputer, the calculations took about 20 minutes to model 80 modes(core, surface, and cladding modes) of the two-core PBF structureschematically illustrated by FIG. 1B at a particular wavelength.

For a triangular cladding lattice, the modes of a single-core PBF havethe symmetries of the point group C_(6v). However, twin-core fiberstructures have two axes of symmetry: one along a line joining both corecenters, (termed the y-axis), and the other along a line orthogonal tothe line joining both core centers (termed the x-axis) and formed by thepoints equidistant from both core centers. Consequently, the modes of atwo-core PBF belong to the C₂ point group, and all their modes can beclassified in one of four representations, defined as:

Representation A1: x-polarized, odd mode;

Representation A2: y-polarized, odd mode;

Representation B1: x-polarized, even mode; and

Representation B2: y-polarized, even mode.

The four fundamental core modes of the two-core PBF fiber 150 can becalculated across the bandgap, and the coupling lengths between the oddand even modes for each polarization can be determined by the effectiveindex differences between the corresponding representations:

$\begin{matrix}{{{L_{C,x}(\lambda)} = \frac{\lambda}{2{{{n_{{eff},{A\; 1}}(\lambda)} - {n_{{eff},{B\; 1}}(\lambda)}}}}}\;{and}\mspace{11mu}\;{{L_{C,y}(\lambda)} = {\frac{\lambda}{2{{{n_{{eff},{A\; 2}}(\lambda)} - {n_{{eff},{B\; 2}}(\lambda)}}}}.}}} & {{Eq}.\mspace{14mu}(1)}\end{matrix}$

An example embodiment of a two-core PBF 150 was modeled using a coreradius R=0.8Λ, a hole radius ρ=0.47Λ of the regions 164 and coreseparations d ranging from Λ to 6Λ in increments of Λ. This core radiusR corresponds to a structure in which each isolated core 170, 180 isfree of surface modes (see, e.g., U.S. Pat. No. 7,110,650, U.S. PatentApplication Publication No. 2005/0281522A1, and H. K. Kim et al.,“Designing air-core photonic-bandgap fibers free of surface modes,” IEEEJ. Quant. Electron., Vol. 40, pages 551-556 (2004), each of which isincorporated in its entirety by reference herein). The calculateddispersion curves of all the core modes that fall within the bandgap,highlighted according to their symmetry class, are plotted in FIG. 2 fora core separation of d=3Λ. This two-core PBF exhibits a bandgap thatextends from 0.56Λ to 0.64Λ, which are identical to the bandgap for asingle-core PBF. Neither the first core 170 nor the second core 180 ofthe two-core PBF supports surface modes, thereby retaining the surfacemode-free properties of the single core structure resulting from theproper choice of core radius, as predicted by the existence criterionpresented by M. J. F. Digonnet et al, “Simple geometric criterion topredict the existence of surface modes in air-core photonic-bandgapfibers,” Optics Express, Vol. 12, pages 1864-1872 (2004).

As illustrated by FIG. 2, both polarizations exhibit a significantbirefringence between the odd and even modes. For example, at awavelength of λ=0.6Λ, the index difference Δn is approximately 6×10⁻⁴for the x-polarization and 4×10⁻⁴ for the y-polarization. The even modeshave a higher effective index than do the odd modes (for this corespacing d=3Λ), similar to the situation prevailing in solid-core fibers(where even modes have a slower phase velocity than do odd modes). For atypical crystal period of Λ=2.5 microns, the coupling lengths calculatedfrom these index differences are L_(c,x)=1.2 millimeters and L_(c,y)=1.9millimeters.

These values are comparable to the coupling lengths of conventionalindex-guiding two-core fibers with similar core spacings. This result issomewhat surprising since the cladding field of the fundamental mode ismuch weaker in an air-core fiber than in a conventional single-modefiber, so the coupling length was consequently expected to besubstantially longer. The direct consequence of this result is that fullcoupling can be achieved between the cores of a two-core PBF overlengths of the order of one millimeter (e.g., a coupling length in arange between approximately 1 millimeter and approximately 1.9centimeters), which means that optical couplers of practical lengths canbe fabricated in hollow-core fibers.

Another property of the two-core PBF illustrated by FIG. 2 is thatcoupling can depend rather strongly on polarization. This feature is notgenerally desirable in certain embodiments in which the polarization ofthe incoming signal has a generally unknown and time-dependent state ofpolarization. However, a side benefit of this strong dependence is thattwo-core PBFs can be used as wavelength-dependent andpolarization-dependent filters, as discussed more fully below.

FIGS. 3A-3H illustrates the calculated intensity profiles of the fourfundamental modes of the two-core PBF (d=3Λ) at λ=0.6Λ. Eachrepresentation is quasi-gaussian in the neighborhood of a core center,and it exhibits small side lobes localized on the thicker regions of thecladding material (e.g., silica) closest to each core. The main lobeshave the same sign for the two even modes, and opposite signs for thetwo odd modes. For d=3Λ, 2=0.6Λ, and Λ=2.5 microns, the coupling lengthfor x-polarized light is about 1.18 millimeters and for y-polarizedlight is about 1.59 millimeters.

Both the x-polarized and y-polarized even modes exhibit some energylocalized around the mid-point between the cores. This property is shownin FIGS. 3C and 3G, but is more readily seen in the logarithmic scaleplots of FIGS. 3D and 3H. The closest opposite sidelobes, for bothcores, are shown to be linked together in FIGS. 3D and 3H, resulting ina stronger effective index for the even modes, and decreased couplinglength. This property results from the presence of a solid membrane atthe mid-point, which is surrounded by hollow regions on both sides andthus constitutes a local index-guided waveguide.

In contrast, the odd modes carry virtually no energy at the mid-pointbetween the cores, as shown in FIGS. 3A and 3E. Therefore, the evenmodes have a larger amount of energy in the solid membrane, which raisestheir effective index relative to the odd modes. This phenomenon is atthe origin of the surprisingly large predicted coupling: the presence ofthe solid membrane at the mid-point between the cores raises theeffective index of the even modes relative to the odd modes, and it doesso by a substantial amount because of the large index difference betweenthe hollow regions and the solid material (e.g., silica). Thisphenomenon also explains why the even modes of this two-core PBF (d=3Λ)have a higher effective index than do the odd modes.

Based on this physical explanation, the coupling strength can beconsiderably smaller when there is a hollow region rather than a solidmembrane at the center of the fiber. This configuration can beaccomplished by changing the core spacing from an odd to an evenmultiple of Λ. FIGS. 4A-4D illustrate the contour intensity profiles ofthe four fundamental modes of the same two-core PBF and at the samewavelength, but for d=4Λ. The mid-point between both cores is nowlocated at the center of a hollow region of the cladding, and thedifferences between the intensity profiles of the odd and even modes aremuch less pronounced. The dispersion curves of the four modes aretherefore much closer to each other than they are for a spacing of d=3Λ,as shown in FIG. 5. The high-index mid-point solid membrane has beenreplaced by a lower index material (e.g., air), and the birefringence ofall modes is noticeably reduced. For d=4Λ, for the x-polarization, therelative position of the dispersion curves for the odd and even modes isreversed from what it is for d=3Λ, as shown by a comparison of FIGS. 2and 5. The order of the dispersion curves of the odd and even modesremains unchanged for the y-polarization by changing from d=3Λ to d=4Λ.

The polarization dependence of the coupling length in a two-core PBF isa feature not present in conventional two-core fibers. In the latter,due to the azimuthal invariance of the refractive index profile, thefields of the two orthogonally polarized fundamental modes differ onlyvery slightly under a 90-degree rotation. Hence, the mode overlap fromone fiber core to the other depends extremely weakly on polarization.This behavior can be seen mathematically in the expression of thecoupling coefficient κ defined as κ=π(2L_(C)), and is given by:

$\begin{matrix}{\kappa = {{\omega ɛ}_{0}\frac{\underset{{core}\; 1}{\int\int}{n^{2}\left( {x,y} \right)}{{\overset{\rightharpoonup}{E}}_{1} \cdot {\overset{\rightharpoonup}{E}}_{2}^{*}}{\mathbb{d}x}{\mathbb{d}y}}{\underset{coupler}{\int\int}{u_{z} \cdot \left( {{{\overset{\rightharpoonup}{E}}_{1}^{*} \times {\overset{\rightharpoonup}{H}}_{1}} + {{\overset{\rightharpoonup}{E}}_{1} \times {\overset{\rightharpoonup}{H}}_{1}^{*}}} \right)}{\mathbb{d}x}{\mathbb{d}y}}}} & {{Eq}.\mspace{14mu}(2)}\end{matrix}$where Ē₁ and H ₁ are the fields of the fundamental mode for the firstcore and Ē₂ and H ₂ are the fields of the fundamental mode for thesecond core. In a single-mode solid-core fiber, both solutions for theorthogonal polarizations are deduced from each other through a 90-degreerotation, so both the numerator and the denominator of Equation (2) arepolarization-independent. This results in the coupling coefficient κbeing essentially independent of polarization. In contrast, in atwo-core PBF, the fundamental modes belong to a two-dimensionalrepresentation and are not invariant under a 90-degree rotation. Thefield distribution of one polarization mode cannot be derived from thedistribution of the other polarization mode through a simple rotation,and the field overlap integral in the numerator of Equation (2) ispolarization-dependent.

FIG. 6 illustrates the normalized coupling length L_(C)/Λ calculatedagainst the normalized wavelength λ/Λ for both the x- andy-polarizations and increasing values of the core separation. Thecoupling length increases rapidly (e.g., approximately exponentially) asthe core separation increases, because the mode energy decreases rapidlyaway from the center of a given core. The coupling length is found toincrease roughly by a factor of 3 to 5 for every increase in d of Λ. Forexample, at 0.6λ/Λ, for x-polarization, L_(c) increases from 1.2millimeters for d=3Λ to 5.5 millimeters for d=4Λ. This rate isconsistent with the fundamental core mode field intensity spatialattenuation in a single-core PBF of similar parameters. The polarizationdependence of the coupling length is again significant, even for largercore separations. For a separation of one period (d=Λ), the two coresstrongly overlap with each other and form a single, roughly “8”-shapedcore elongated along the y-axis, which explains the reduced polarizationdependence. The anomalous behavior for d=2Λ is also believed to becaused by overlap between the cores, For d=3Λ, which is the shortestpossible separation along the y-axis without core overlap, thewavelength dependence is relatively strong. Across the bandgap, thecoupling length varies by about a factor of about 4.

Two-core PBFs also exhibit different modal behavior than conventionaltwo-core fibers. In typical fiber coupler structures made withindex-guiding fibers, the even mode exhibits a higher effective indexthan does the odd mode. In contrast, due to the presence of either ahollow region or a solid material at the middle point between both fibercores (depending on the core separation d), the parity of d/Λ determinesthe modal behavior of the two-core PBF structures. For even values ofd/Λ, the middle point between the two cores is at a hollow region, andfor odd values of d/Λ, the middle point between the two cores is locatedin the solid cladding material. Depending on the parity of d/Λ, therelative positions of the odd and even fundamental core modes of thetwo-core PBF structure are exchanged, as shown in FIGS. 2 and 5. For oddvalues of d/Λ, the even fundamental mode has a higher effective indexthan does the odd mode, regardless of polarization, as in the case of aconventional index-guiding two-core fiber. However, for even values ofd/Λ, the odd fundamental mode has a higher effective index than the evenmode for the x-polarization, while that behavior is opposite for they-polarization.

As shown in FIGS. 3C and 3G, the even x-polarized mode of representationA2 shows a linking of the closest sidelobes across the y-axis. The eveny-polarized mode of representation B2 exhibits some energy locatedwithin the solid membrane located at the mid-point. The combination ofsolid material at the mid-point with hollow regions on both sides formsa waveguide locally, and the even modes of the two-core PBF structurecan concentrate a larger amount of energy in the solid membrane, thusraising their effective index. This observation explains the unique PBFfeature of the even modes of the two-core PBF structure having a highereffective index than does the odd modes for odd values of thecore-to-core spacing parameter d/Λ. For even values of the core-to-corespacing parameter d/Λ, the mid-point between both cores is located in ahollow region, and the differences between odd and even mode intensityprofiles are much smaller.

In certain embodiments, the two-core PBF can be used as a four-portfiber coupler 100, as schematically illustrated by FIG. 1A. The opticalcoupler 100 can be only a few millimeters in length and can provide fullcoupling between the ports. FIG. 7A illustrates the performance of anexample optical coupler 100 by plotting the coupling ratio for atwo-core PBF 150 with a crystal period Λ=2.6 microns, such that thebandgap is centered around 1.55 microns, with d=3Λ=7.8 microns and alength L=10.5 millimeters. The coupling ratio is plotted for both x- andy-polarized light. In certain embodiments having a sizable wavelengthdependence, the optical coupler 100 can be used as a wavelength-divisionmultiplexer with the same input polarization restrictions. Thewavelength separation between 0 and 100% coupling ranges from about 18nanometers to about 32 nanometers for the x-polarization, and from about26 nanometers to about 42 nanometers for the y-polarization. To beuseable over a broad range of wavelengths, in certain embodiments, theinput polarization is advantageously maintained to be stable, forexample by circuits using polarization-maintaining fiber.

In certain embodiments, the two-core PBF 150 can be used as apolarization-independent directional optical coupler at any of thewavelengths where the two curves of FIG. 7A intersect. For example, thetwo-core PBF 150 can be used as an approximately 3-dB fiber coupler at1584 nanometers (point A of FIG. 7A), and an approximately 100% couplerat 1522 nanometers (point B of FIG. 7A). In the vicinity of point B, thecoupling ratio exceeds 90% over a bandwidth of about 5 nanometers.Either the wavelengths or the coupling ratios at the crossing points canbe adjusted to desired values by proper selection of the length of thetwo-core PBF 150.

The polarization dependence of the two-core PBF 150 can also beexploited in certain embodiments to be used as either a fiber polarizer,a polarization splitter at discrete wavelengths, or a polarizationsensor. Based on the curves of FIG. 7A, at 1569 nanometers (point C ofFIG. 7A, magnified in FIG. 7C), x-polarized light comes out of one coreor port and y-polarized light comes out of the other core or port. The10-dB and 20-dB bandwidths are approximately 10 nanometers and 4nanometers, respectively. Similar bandwidths are obtained at 1599nanometers (point D of FIG. 7A, magnified in FIG. 7D), except that theroles of the polarizations are switched.

In certain embodiments, the center wavelengths can be adjusted byselecting the coupler length appropriately. FIGS. 8A and 8B illustratethe transmission as a function of wavelength for both polarizations inexample two-core PBFs with lengths of 2 millimeters and 3 millimeters,respectively. Other geometrical parameters can also be adjusted todesign a coupler with the desired coupling properties. In certainembodiments, one or both of the cores has a thin ring of the firstmaterial (e.g., silica) surrounding the core. A calculation of thecoupling length for a two-core PBF with a core ring of thicknesst=0.025Λ showed a polarization-dependent change in coupling. Forexample, for d=3Λ, λ=0.6Λ, and A=2.5 microns, the coupling length forx-polarization decreased from 1.2 millimeters to 0.6 millimeters byadding the core ring, while the coupling length for y-polarizationincreased from 1.9 millimeters to 2.9 millimeters. This change may haveoriginated from a modification in the mode field distribution towardsthe edge of the core when a ring is present, which modifies the overlapbetween the core modes and thus the coupling. Similarly, increasing theair-filling ratio of the fiber increases the coupling length. Forexample, for d=3Λ and at λ=1.5 microns at the center of the bandgap,when the cladding hollow region radius was increased from ρ=0.47Λ toρ=0.49Λ (a typical value for commercial PBFs), the x-polarizationcoupling length increased from 1.2 millimeters to 2.7 millimeters andthe y-polarization coupling length increased from 1.9 millimeters to 2.9millimeters.

In certain embodiments, the wavelength at which the x-polarization andy-polarization coupling lengths intersect (e.g., the wavelength at whichthe two-core PBF can be used as a polarization-independent directionalcoupler) can be selected by tailoring the core radius. This behavior isillustrated by FIG. 9 which shows the x- and y-polarization couplinglengths for various values of the core radius R as functions ofwavelength. In certain embodiments in which the coupling length as afunction of wavelength has an inflection point at which the slope iszero, the two-core PBF can be used as a broadband polarizer over a rangeof wavelengths.

FIGS. 10A and 10B schematically illustrate two example two-core PBFs 150compatible with certain embodiments described herein. Each of thesestructures can increase the coupling coefficient for larger coreseparations. FIG. 10A schematically illustrates a point defect 190between the two cores 170, 180 and FIG. 10B schematically illustrates aline defect 192 between the two cores 170, 180. In certain embodiments,the propagation properties of the two-core PBF 150 are strongly affectedby the structure of the defect between the two cores 170, 180.

FIG. 11 illustrates the birefringence as a function of the defect radiusfor the point defect 190 of FIG. 10A with a core separation of 4 crystalspatial periods. An increase of the coupling coefficient by about afactor of 20 is possible, and discontinuities due to interactions withsurface modes are supported by the defect. FIG. 12 illustrates thebirefringence as a function of the defect radius for the point defect190 of FIG. 10A with a core separation of 6 crystal spatial periods. Anincrease of the coupling coefficient by about a factor of 10 ispossible, and there is a high sensitivity to the defect radius whenthere are interactions with surface modes.

FIG. 13 illustrates the birefringence as a function of the defect radiusfor the line defect 192 of FIG. 10B with a core separation of 6 crystalspatial periods. An increase of the coupling coefficient by about afactor of 1000 is possible, and there is a high sensitivity to thedefect size in specific areas. In certain embodiments, the two-core PBFis operated at a wavelength at which the transmission is very stronglydependent on the defect size. The signal transmitted through thetwo-core PBF in certain such embodiments would exhibit a strongvariation due to any perturbation of the defect size, and could serve asa sensor for any effects (e.g., pressure waves) that would perturb thedefect size.

Various embodiments of the present invention have been described above.Although this invention has been described with reference to thesespecific embodiments, the descriptions are intended to be illustrativeof the invention and are not intended to be limiting. Variousmodifications and applications may occur to those skilled in the artwithout departing from the true spirit and scope of the invention asdefined in the appended claims.

1. An optical fiber comprising: a cladding; a first core; a second core,wherein at least a portion of the first core is generally parallel toand spaced from at least a portion of the second core such that thefirst core is optically coupled to the second core, wherein at least oneof the first core and the second core is hollow and is substantiallysurrounded by the cladding; and a defect substantially surrounded by thecladding, the defect increasing a coupling coefficient between the firstcore and the second core, the defect between the first core and thesecond core and spaced from both the first core and the second core. 2.The optical fiber of claim 1, wherein the cladding comprises a materialwith a first refractive index and regions within the cladding, theregions having a second refractive index lower than the first refractiveindex.
 3. The optical fiber of claim 2, wherein the regions are hollow.4. The optical fiber of claim 2, wherein the regions each have arespective center and adjacent regions are spaced apart in a periodicpattern having a spatial period.
 5. The optical fiber of claim 4,wherein the first core and the second core have a center-to-centerdistance that is substantially equal to an integer multiple of thespatial period.
 6. The optical fiber of claim 1, wherein the first coredoes not support surface modes and the second core does not supportsurface modes.
 7. The optical fiber of claim 1, wherein the opticalcoupling between the first core and the second core ispolarization-dependent.
 8. The optical fiber of claim 1, wherein thefirst core and the second core have a coupling length in a range betweenapproximately 1 millimeter and approximately 1.9 centimeters.
 9. Theoptical fiber of claim 1, wherein at least one of the first core and thesecond core comprises a core ring.
 10. The optical fiber of claim 1,wherein the defect comprises a point defect on a central hole of thecladding.
 11. The optical fiber of claim 1, wherein the defect comprisesa linear defect.
 12. A method for using an optical fiber, the methodcomprising: providing an optical fiber comprising: a first core; asecond core spaced from the first core and optically coupled to thefirst core; a defect configured to increase a coupling coefficientbetween the first core and the second core, the defect between the firstcore and the second core and spaced from both the first core and thesecond core; and a cladding substantially surrounding the defect and atleast one of the first core and the second core; and coupling lightbetween the first core and the second core.
 13. The method of claim 12,further comprising using the optical fiber as a polarization-dependentoptical coupler.
 14. The method of claim 12, further comprising usingthe optical fiber as a polarization-independent optical coupler.
 15. Themethod of claim 12, further comprising using the optical fiber as awavelength-division multiplexer.
 16. The method of claim 12, furthercomprising using the optical fiber as a fiber polarizer.
 17. The methodof claim 12, further comprising using the optical fiber as apolarization splitter.
 18. The method of claim 12, wherein the at leastone of the first core and the second core is hollow.
 19. Aphotonic-bandgap fiber comprising: a first core; a second core opticallycoupled to the first core, wherein at least a portion of the second coreis generally parallel to and spaced from at least a portion of the firstcore, wherein at least one of the first core and the second core ishollow; a defect increasing a coupling coefficient between the firstcore and the second core, the defect between the first core and thesecond core and spaced from both the first core and the second core; anda cladding substantially surrounding the defect and the at least one ofthe first core and the second core.
 20. The fiber of claim 19, whereinthe first core does not support surface modes and the second core doesnot support surface modes.
 21. The fiber of claim 19, wherein theoptical coupling between the first core and the second core ispolarization-dependent.
 22. The fiber of claim 19, wherein both of thefirst core and the second core are hollow.
 23. The fiber of claim 19,wherein the defect comprises a point defect.
 24. The fiber of claim 19,wherein the defect comprises a linear defect.